What is a good fingering to use to be able to play through chromatic scales of a run-like-nature on the piano? For instance, I find that using the usual 1-2-3-1-3-1-3 fingering (assuming I'm using my right hand) that I've been taught in the ABRSM curriculum seems to be pretty ineffective in passages with long chromatic runs such as that at the very end of the first Grave section in Beethoven's Pathetique.

1 Answer
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Starting from C and going up, there's the standard 1/2 3 1 3 1 2 3 1 3 1 3 1 2. This is usually enough. With practice it should work for that particular run in Beethoven.

The trick to make things faster is to use longer groupings. With the above fingering most groups are (1 3) and some are (1 2 3). So, let's use (1 2 3) and (1 2 3 4) instead. Starting from C and going up, try (1 2 3 4) (1 2 3) (1 2 3 4) (1 2 3) (1 2 3) (1 2 3 4) (1 ...). Note that the pattern is different every other octave. Getting that to work requires some practice in itself but the result should be a faster and smoother run.